Procedures for analyzing multicomponent FT-IR spectra for unknown mixtures of gases

A procedure for analyzing a multicomponent FT-IR spectrum of an unknown mixture of gases, the procedure comprising the steps of:

• providing a gas spectrum analyzer in which a set of FT-IR library spectra of pure molecular gases, measured in known pressures, are stored as vectors k having N components and by which analyzer inner products for all possible combinations of two vectors k are calculated and stored;
• measuring an FT-IR spectrum s for the unknown mixture of gases;
• storing by said gas spectrum analyzer the FT-IR spectrum s as a vector having N components;
• selecting from said set of stored FT-IR library spectra of pure molecular gases those M gases which are expected to be contained in the unknown mixture of gases;
• forming from the library vectors k of the selected M gases a basis matrix K;
• forming an orthogonal basis matrix K' by deforming the vectors k chosen for the matrix K to orthogonal vectors k' so that inner products of these vectors k' with each other but not with themselves are zero;
• calculating and storing the inner products of said orthogonal vectors k' with themselves;
• forming and storing a basis transformation matrix Q so that K=K'Q;
• forming and storing an inverse matrix Q.sup.-1 of the matrix Q;
• calculating an optimal coefficient vector x' for the spectrum s of the unknown mixture of gases in the orthogonal basis by using for its components x.sub.j ' the equation ##EQU35## calculating a coefficient vector x so that x=Q.sup.-1 X';
• calculating partial pressures of the pure gases in the unknown mixture of gases by multiplying the measuring pressures of the selected library spectra by their coefficients x.sub.j thus forming an analysis result for the unknown mixture of gases in the form of the partial pressures of those pure molecular gases expected to be contained in said unknown mixture of gases;
• and
• comparing the vector representing the measured spectrum s to its analysis result in order to evaluate the analysis result and thus the successfulness of selection of the pure molecular gases expected to be contained in said unknown mixture of gases.